Improvements in or relating to converters for use in high voltage direct current power transmission

ABSTRACT

In the field of high voltage direct current (HVDC) power transmission, a converter comprises three converter limbs, each corresponding to a respective phase of the converter, each extending between first and second DC terminals and each including first and second limb portions separated by an AC terminal. Each limb portion includes a chain-link converter that is operable to provide a stepped variable voltage source, and a primary switching element to selectively switch the respective limb portion into and out of circuit. The converter also includes a first controller that is programmed to selectively operate for one converter limb at a time the primary switching element in each limb portion thereof to simultaneously switch both the first and second limb portions into circuit and thereby define a fully-conducting converter limb to sequentially route via each said fully-conducting converter limb a DC current demand (I DC ) between the first and second DC terminals.

This invention relates to a converter for use in high voltage direct current power transmission.

In high voltage direct current (HVDC) power transmission networks alternating current (AC) power is typically converted to direct current (DC) power for transmission via overhead lines and/or under-sea cables. This conversion removes the need to compensate for the AC capacitive load effects imposed by the power transmission medium, i.e. the transmission line or cable, and reduces the cost per kilometre of the lines and/or cables, and thus becomes cost-effective when power needs to be transmitted over a long distance.

The conversion between DC power and AC power is utilized in power transmission networks where it is necessary to interconnect the DC and AC electrical networks. In any such power transmission network, converters are required at each interface between AC and DC power to effect the required conversion; AC to DC or DC to AC.

According to a first aspect of the invention there is provided a converter, for use in high voltage direct current power transmission, comprising:

-   -   three converter limbs, each corresponding to a respective phase         of the converter, each extending between first and second DC         terminals and each including first and second limb portions         separated by an AC terminal, each limb portion including a         chain-link converter operable to provide a stepped variable         voltage source and a primary switching element to selectively         switch the respective limb portion into and out of circuit; and     -   a first controller programmed to selectively operate for one         converter limb at a time the primary switching element in each         limb portion thereof to simultaneously switch both the first and         second limb portions into circuit and thereby define a         fully-conducting converter limb to sequentially route via each         said fully-conducting converter limb a DC current demand between         the first and second DC terminals.

Sequentially routing, via each fully-conducting converter limb in turn, a DC current demand between the first and second DC terminals allows the DC current demand to flow continuously between the first and second DC terminals, and thereby permits the converter of the invention to continuously exchange power with a DC network, connected in use with the first and second DC terminals, throughout an operating cycle of the converter.

Meanwhile, having only one fully-conducting converter limb at a time avoids the creation of current paths between respective converter limbs, and so no transient circulating currents between converter limbs arise. The absence of such circulating currents permits the removal of a passive inductor from each limb portion that would otherwise be needed to limit the level of aforementioned circulating current between the converter limbs.

Such passive inductors are physically very large, and so omitting them allows for a significant reduction, e.g. of around 20%, in the overall footprint of a converter station including the converter of the invention. This in turn helps to reduce considerably the cost of the converter station.

In addition, omitting the passive inductor from each limb portion also means that it is possible to connect a transformer directly with the converter without the need for interconnecting bushings which are typically large and expensive, and so offers further space- and cost-saving opportunities.

In addition, omitting an inductor from each limb portion allows for an increase in the level of AC voltage that can be generated by the converter, while permitting a reduction in the level of AC current, i.e. the level of individual AC current demand phase waveforms, that must be provided, and so gives rise to an increase in the efficiency of the converter.

Preferably the first controller is programmed to sequentially define fully-conducting converter limbs at regular intervals of around 60 electrical degrees.

The inclusion of a first controller so programmed results in the DC current demand routed between the first and second DC terminal being smooth and continuous.

Optionally the first controller is additionally programmed, while selectively operating for a given converter limb the primary switching element in each limb portion thereof to simultaneously switch both the first and second limb portions into circuit and thereby define a fully-conducting converter limb, to concurrently operate for each other converter limb the primary switching element in one or both limb portions thereof to switch a single limb portion into circuit and thereby define a partially-conducting converter limb to direct respective AC current demand phase waveforms towards a given AC terminal whereby the respective AC current demand phase waveforms sum to zero.

Having the AC current demand phase waveforms sum to zero at a given AC terminal, i.e. within the converter of the invention, eliminates the inclusion of any AC components in the DC current demand routed between the first and second DC terminals, and so avoids the need to filter this current before, e.g. passing it to a DC network connected in use to the first and second DC terminals.

Any kind of filter in a HVDC installation has major implications with regards to the footprint of a resulting converter station, and so avoiding such filters is very beneficial.

A converter according to preferred embodiment of the invention further includes a second controller programmed to:

-   -   (a) obtain a respective AC current demand phase waveform for         each converter limb which the corresponding converter limb is         required to track, and a DC current demand which each converter         limb is also required to track; and     -   (b) carry out mathematical optimization to determine an optimal         limb portion current for each limb portion that the limb portion         must contribute to track the corresponding required AC current         demand phase waveform and the required DC current demand.

Carrying out the aforementioned mathematical optimization, i.e. selecting the best individual limb portion current (with regard to chosen criteria) from a set of available alternatives, allows the AC and DC current demands to be controlled independently of one another, e.g. by a higher level controller.

It also permits individual limb portion currents to vary independently of one another to accommodate different current flow paths through the converter, e.g. as occasioned by the sequential definition of a fully-conducting converter limb and respective partially-conducting converter limbs throughout each operating cycle of the converter.

Moreover, the second controller is able to carry out steps (a) and (b) in real time so as to permit robust control of the converter of the invention.

The second controller may be programmed to carry out mathematical optimization by creating an equivalent converter configuration which represents the flow of current through the converter.

Creating an equivalent converter configuration in the aforementioned manner imposes constraints on the way in which the converter can be controlled and so assists in carrying out mathematical optimization to determine each optimal limb portion current.

Optionally the second controller is programmed to create an equivalent converter configuration which represents the flow of current through the converter by mapping possible current flow paths through the converter.

Mapping the possible current flow paths through the converter helps the second controller to tailor the mathematical optimization it provides to the topology, i.e. structure, of the converter of the invention.

Preferably the second controller is programmed to carry out mathematical optimization by applying a current weighting to the relative current contribution provided by a plurality of limb portions.

Applying such weightings allows variations in the performance of each limb portion to be further accommodated while continuing to optimise the operation of the converter as a whole.

The second controller may be programmed to determine the or each weighting according to measured operating parameters of the converter.

Determining the weightings in the aforementioned manner allows the second controller to take into account environmental factors which might affect the healthy operation of the converter, and to alter the optimal limb portion currents that are determined in an effort to overcome the environmental factors and alleviate the associated impact on the operation of the converter. Examples of such environmental factors include the components in one limb portion running hot, or a limb portion suffering component damage or failure such that its performance is degraded.

In another preferred embodiment of the invention the second controller, when controlling the converter under a particular operating condition, is programmed to apply a weighting by applying a different weighting to at least one limb portion such that the or each said limb portion provides a different contribution to the other limb portions.

Such a feature allows the second controller to distinguish between one limb portion and another, e.g. according to how well a given limb portion is performing.

This is useful in circumstances where it becomes desirable to reduce the level of current contributed by a given limb portion, e.g. because the cooling associated with the limb portion is operating at a reduced capacity, and temporarily increase the level of current provided by one or more other limb portions so as to allow the converter to continue to operate and provide a high level of power conversion.

It can also be used to reduce the limb portion voltage that a given limb portion must provide, e.g. in circumstances where a fault or other damage has degraded the performance of the given limb portion, such that the converter remains able to continue operating and provide a high level of power conversion.

Preferably the second controller is programmed to carry out mathematical optimization to determine one or more minimum individual limb portion currents that the corresponding limb portion must contribute to track the corresponding required AC current demand phase waveform and the required DC current demand.

Determining one or more minimum individual limb portion currents reduces the conduction and switching losses in each limb portion because ordinarily such losses are proportional to current squared, i.e. I².

In a still further preferred embodiment of the invention the second controller is further programmed to carry out mathematical optimization to provide optimal limb portion voltage sources.

The inclusion of a second controller so programmed assists in the provision, in the most efficient manner possible, of individual limb portion currents that vary independently of one another.

There now follows a brief description of preferred embodiments of the invention, by way of non-limiting example, with reference being made to the following figures in which:

FIG. 1 shows a schematic view of a converter according to a first embodiment of the invention;

FIG. 2 shows a preferred switching sequence of primary switching elements within the converter shown in FIG. 1 during an operating cycle of the converter;

FIG. 3 illustrates schematically the selective definition of a fully-conducting converter limb and respective partially-conducting converter limbs in the converter shown in FIG. 1;

FIG. 4 shows a flow diagram that illustrates the principal steps a second controller in the converter shown in FIG. 1 is programmed to carry out;

FIG. 5 shows a schematic representation of an equivalent converter configuration corresponding to the converter shown in FIG. 1;

FIG. 6(a) shows a flow diagram that illustrates the principal steps a further second controller may be programmed to carry out; and

FIG. 6(b) shows a schematic view of a feedback loop which forms a part of the principal steps the further controller may be programmed to carry out.

A converter according to a first embodiment of the invention is designated generally by reference numeral 10, as shown in FIG. 1.

The converter 10 includes three converter limbs 12A, 12B, 12C, each of which corresponds to a respective phases A, B, C of the converter 10.

Each converter limb 12A, 12B, 12C extends between first and second DC terminals 14, 16, and each converter limb 12A, 12B, 12C includes a first limb portion 12A+, 12B+, 12C+ and a second limb portion 12A−, 12B−, 12C− which are separated by an AC terminal 18A, 18B, 18C.

In use, the first and second DC terminals 14, 16 are connected to a DC network 20, with the first DC terminal 14 carrying a voltage of V_(DC+) and the second DC terminal 16 carrying a voltage of V_(DC−), while the AC terminal 18A, 18B, 18C is connected to a corresponding phase A, B, C of a three-phase AC network 22 and carries a corresponding AC voltage phase waveform V_(A), V_(B), V_(C).

Each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− includes a chain-link converter 24A+, 24A−, 24B+, 24B−, 24C+, 24C− that includes a chain of modules 26 connected in series. The number of modules 26 in each chain-link converter 24A+, 24A−, 24B+, 24B−, 24C+, 24C− depends on the required voltage rating of the respective limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−.

Each module 26 of each chain-link converter 24A+, 24A−, 24B+, 24B−, 24C+, 24C− includes two pairs of secondary switching elements (not shown) connected in parallel with an energy storage device, in the form of a capacitor (not shown), to define a 4-quadrant bipolar module 26 that can provide negative, zero or positive voltage and can conduct current in two directions.

In use, the secondary switching elements of the modules 26 of each chain-link converter 24A+, 24A−, 24B+, 24B−, 24C+, 24C− are operated to enable each chain-link converter 24A+, 24A−, 24B+, 24B−, 24C+, 24C− to provide a stepped variable voltage source. The secondary switching elements are also desirably switched at near to the fundamental frequency of the AC network 22.

The capacitor of each module 26 may be bypassed or inserted into the respective chain-link converter 24A+, 24A−, 24B+, 24B−, 24C+, 24C− by changing the state of the secondary switching elements.

The capacitor of each module 26 is bypassed when the pairs of secondary switching elements are configured to form a short circuit in the module 26. This causes current in the corresponding limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− of the converter 10 to pass through the short circuit and bypass the capacitor, and so the module 26 is able to provide a zero voltage.

The capacitor of each module 26 is inserted into the respective chain-link converter 24A+, 24A−, 24B+, 24B−, 24C+, 24C− when the pair of secondary switching elements is configured to allow the aforementioned current to flow into and out of the capacitor. The capacitor is then able to charge or to discharge its stored energy so as to provide a voltage. The bidirectional nature of the 4-quadrant bipolar module 26 means that the capacitor may be inserted into the module 26 in either forward or reverse directions so as to provide a positive or negative voltage.

It is therefore possible to build up a combined voltage across each chain-link converter 24A+, 24A−, 24B+, 24B−, 24C+, 24C− which is higher than the voltage available from each individual module 26 via the insertion of the capacitors of multiple modules 26, each providing its own voltage, into the chain-link converter 24A+, 24A−, 24B+, 24B−, 24C+, 24C−.

The ability of a 4-quadrant bipolar module 26 to provide positive or negative voltages means that the voltage across each chain-link converter 24A+, 24A−, 24B+, 24B−, 24C+, 24C− may be built up from a combination of modules 26 providing positive or negative voltages. The energy levels in individual capacitors may be maintained therefore at optimal levels by controlling the modules 26 to alternate between providing positive or negative voltage.

It is possible to vary the timing of switching operations for each module 26 such that the insertion and/or bypass of the capacitors of individual modules 26 in the chain-link converter 24A+, 24A−, 24B+, 24B−, 24C+, 24C− results in the generation of a voltage waveform at a corresponding AC terminal 18A, 18B, 18C. For example, insertion of the capacitors of the individual modules 26 may be staggered to generate a sinusoidal waveform. Other waveform shapes may be generated by adjusting the timing of switching operations for each module 26 in the chain-link converter 24A+, 24A−, 24B+, 24B−, 24C+, 24C−.

In this manner the chain-link converters 24A+, 24A−, 24B+, 24B−, 24C+, 24C− are able to facilitate power transfer between the AC and DC networks 22, 20.

In addition to the foregoing, the inclusion of 4-quadrant bipolar modules 26 means that it is possible for each chain-link converter 24A+, 24A−, 24B+, 24B−, 24C+, 24C− to block a DC fault current in the event of e.g. a pole to pole fault in the DC network 20, with such blocking being achieved by opening appropriate secondary switching elements in each module 26 to prevent the flow of fault current through each said module 26.

Each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− also includes a primary switching element Sw₁, Sw₄, Sw₃, Sw₆, Sw₅, Sw₂ that is connected in series with the corresponding chain-link converter 24A+, 24A−, 24B+, 24B−, 24C+, 24C−. In use, each primary switching element Sw₁, Sw₂, Sw₃, Sw₄, Sw₅, Sw₆ selectively switches the respective limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− into and out of circuit within the converter 10.

In other embodiments of the invention (not shown) each primary switching element may include a plurality of, e.g. series-connected, switching elements depending on the required voltage rating of each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−.

In addition, the series connection between each primary switching element Sw₁, Sw₂, Sw₃, Sw₄, Sw₅, Sw₆ and the corresponding chain-link converter 24A+, 24A−, 24B+, 24B−, 24C+, 24C− in each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− allows, in other embodiments of the invention, the respective primary switching element Sw₁, Sw₂, Sw₃, Sw₄, Sw₅, Sw₆ and corresponding chain-link converter 24A+, 24A−, 24B+, 24B−, 24C+, 24C− to be connected in a reverse order between the corresponding AC terminal 18A, 18B, 18C and the respective first or second DC terminal 14, 16.

In the embodiment shown, each primary switching element Sw₁, Sw₂, Sw₃, Sw₄, Sw₅, Sw₆ and each of the secondary switching elements in the respective chain-link converters 24A+, 24A−, 24B+, 24B−, 24C+, 24C− is an insulated gate bipolar transistor (IGBT) 28 connected in parallel with an anti-parallel diode 30.

In other embodiments of the invention (not shown) one or more of the primary and secondary switching elements Sw₁, Sw₂, Sw₃, Sw₄, Sw₅, Sw₆ may include a different semiconductor device, such as a field effect transistor, a gate-turn-off thyristor, an injection gate enhanced thyristor, an integrated gate commutated transistor or another externally-commutated semiconductor switch, i.e. a semiconductor switch which is turned off by one or more external components causing the current flowing through the semiconductor switch to fall to zero. Such other externally-commutated semiconductor switches can include so-called ‘forced commutated’ and ‘self commutated’ semiconductor switches. In each instance the semiconductor device is preferably connected in parallel with an anti-parallel diode.

For the reasons set out hereinabove, each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− omits any form of physical, passive inductor component, which in turns provides considerable benefits in terms of reducing the overall footprint of a resulting converter station in which the converter of the invention is incorporated.

In addition to the foregoing, the converter 10 includes a first controller 32 that is arranged in operative communication with each primary switching element Sw₁, Sw₂, Sw₃, Sw₄, Sw₅, Sw₆.

The first controller 32 is a programmable device, such as a microcontroller, and more particularly is programmed to operate, for one converter limb 12A, 12B, 12C at a time, the primary switching element Sw₁, Sw₂, Sw₃, Sw₄, Sw₅, Sw₆ in each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− thereof to simultaneously switch both the first limb portions 12A+, 12B+, 12C+ and the second limb portions 12A−, 12B−, 12C− into circuit and thereby define a fully conducting converter limb 12A, 12B, 12C.

In this way the first controller 32 sequentially routes, via each said fully-conducting converter limb 12A, 12B, 12C, a DC current demand I_(DC) (i.e. the DC current that the converter limbs 12A, 12B, 12C are required to track) between the first and second DC terminals 14, 16.

More particularly still, the first controller 32 is programmed to sequentially define fully-conducting converter limbs 12A, 12B, 12C at regular intervals 34 ₁, 34 ₂, 34 ₃, 34 ₄, 34 ₅, 34 ₆ of around 60 electrical degrees. In this regard, in an ideal case each interval is 60 electrical degrees, although for practical implementation purposes each interval can lie in the ranges 60±1 electrical degrees, or 60±2 electrical degrees.

The first controller 32 is also additionally programmed, while selectively operating for a given converter limb 12A, 12B, 12C the primary switching element Sw₁, Sw₂, Sw₃, Sw₄, Sw₅, Sw₆ in each limb portion thereof 12A+, 12A−, 12B+, 12B−, 12C+, 12C− to simultaneously switch both the first and second limb portions 12A+, 12B+, 12C+, 12A−, 12B−, 12C− into circuit and thereby define a fully-conducting converter limb 12A, 12B, 12C, to concurrently operate for each other converter limb 12A, 12B, 12C the primary switching element Sw₁, Sw₂, Sw₃, Sw₄, Sw₅, Sw₆ in one or both limb portions 12A+, 12A−, 12B+, 12B−, 12C+, 12C− thereof to switch a single limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− into circuit and thereby define a partially-conducting converter limb 12A, 12B, 12C.

In this manner the first controller 32 is programmed to direct respective AC current demand phase waveforms I_(A), I_(B), I_(C), i.e. respective AC phase currents that the converter 10 is required to track, towards a given AC terminal 18A, 18B, 18C whereby the AC current demand phase waveforms I_(A), I_(B), I_(C) sum to zero.

FIG. 2 shows one example switching sequence of the primary switching elements Sw₁, Sw₂, Sw₃, Sw₄, Sw₅, Sw₆ which is implemented by the first controller 32. Other switching sequences may, however, also be implemented.

In the embodiment shown, the first controller 32 utilises a phase locked loop (PLL) control scheme to coordinate the switching sequence with respective AC voltage phase waveforms V_(A), V_(B), V_(C) of the AC network 22.

More particularly, during a first interval 34 ₁ the first controller 32 operates the primary switching element Sw₁, Sw₄ in each limb portion 12A+, 12A− of a first converter limb 12A to simultaneously switch both the first and second limb portions 12A+, 12A− into circuit and thereby define a fully-conducting converter limb 12A.

At the same time, i.e. concurrently with the foregoing, the first controller 32 operates the primary switching element Sw₆ in the second limb portion 12B− of a second converter limb 12B to switch the second limb portion 12B− into circuit and thereby define a partially-conducting converter limb 12B. The primary switching element Sw₃ in the first limb portion 12B+ of the second converter limb 12B remains switched out of circuit.

The first controller 32 also, at the same time, operates the primary switching element Sw₅ in the first limb portion 12C+ of a third converter limb 12C to switch the first limb portion 12C+ into circuit and thereby define another partially-conducting converter limb 12C. The primary switching element Sw₂ in the second limb portion 12C− of the third converter limb 12C remains switched out of circuit.

During a second interval 34 ₂ the first controller 32 leaves the first limb portion 12C+ of the third converter limb 12C switched into circuit while operating the primary switching element Sw₂ in the second limb portion 12C− of the third converter limb 12C to switch the second limb portion 12C− into circuit and thereby define a fully-conducting converter limb 12C. At the same time the first controller leaves the first limb portion 12A+ of the first converter limb 12A switched into circuit while operating the switching element Sw₄ in the second limb portion 12A− to switch the second limb portion 12A− out of circuit and thereby define a partially-conducting converter limb 12A. The first controller 32 also, at the same time, leaves the second limb portion 12B− of the second converter limb 12B switched into circuit to continue to define a partially-conducting converter limb 12B. The primary switching element Sw₃ in the first limb portion 12B+ of the second converter limb 12B remains switched out of circuit.

During a third interval 34 ₃ the first controller 32 operates the primary switching element Sw₃ in the first limb portion 12B+ of the second converter limb 12B to switch the first limb portion 12B+ into circuit and thereby define, along with the already switched into circuit second limb portion 12B−, a fully-conducting converter limb 12B. At the same time the first controller 32 continues to leave the first limb portion 12A+ of the first converter limb 12A switched into circuit and the second limb portion 12A− of the second limb portion 12A− switched out of circuit to continue to define a partially-conducting converter limb 12A. The first controller 32 also, at the same time, leaves the second limb portion 12C− of the third converter limb 12C switched into circuit while operating the switching element Sw₅ in the first limb portion 12C+ of the third converter limb 12C to switch the first limb portion 12C+ out of circuit to thereby define a partially-conducting converter limb 12C.

During a fourth interval 34 ₄ the first controller 32 operates the primary switching element Sw₄ in the second limb portion 12A− of the first converter limb 12A to switch the second limb portion 12A− into circuit and thereby define, along with the already switched into circuit first limb portion 12A+, a fully-conducting converter limb 12A, as shown by way of example in FIG. 3. As also shown in FIG. 3, the aforesaid fully-conducting converter limb 12A routes a DC current demand I_(DC) between the first and second DC terminals 14, 16.

At the same time the first controller 32 continues to leave the first limb portion 12B+ of the second converter limb 12B switched into circuit while operating the switching element SW₆ of the second limb portion 12B− of the second converter limb 12B to switch the second limb portion 12B− out of circuit to thereby define a partially-conducting converter limb 12B, as also shown in FIG. 3. As additionally shown in FIG. 3, the partially-conducting converter limb 12B, i.e. the first limb portion 12B+ thereof, directs an AC current demand phase waveform I_(B), i.e. an AC phase current I_(B), towards a first AC terminal 18A.

The first controller 32 also, at the same time, leaves the first limb portion 12C+ of the third converter limb 12C switched out of circuit and the second limb portion 12C− of the third converter limb 12C switched into circuit to continue to define a partially-conducting converter limb 12C, as again shown in FIG. 3. As shown in FIG. 3, the partially conducting converter limb 12C, i.e. the second limb portion 12C− thereof, also directs an AC current demand phase waveform I_(C), i.e. an AC phase current I_(C), towards the first AC terminal 18A.

Each of the aforementioned AC current demand phase waveforms I_(B), I_(C), together with a further AC current demand phase waveform I_(A) sum to zero at the first AC terminal 18A, and thereby cancel one another out such that they do not impact adversely on the quality, i.e. smoothness, of the DC current demand I_(DC) routed between the first and second DC terminals 14, 16.

During a fifth interval 34 ₅ the first controller 32 operates the primary switching element Sw₅ in the first limb portion 12C+ of the third converter limb 12C to switch the first limb portion 12C+ into circuit and thereby define, along with the already switched into circuit second limb portion 12C−, a fully-conducting converter limb 12C. At the same time the first controller 32 continues to leave the second limb portion 12A− of the first converter limb 12A switched into circuit while operating the switching element Sw₁ of the first limb portion 12A+ of the first converter limb 12A to switch the first limb portion 12A+ out of circuit to thereby define a partially-conducting converter limb 12A. The first controller 32 also, at the same time, leaves the first limb portion 12B+ of the second converter limb 12B switched into circuit and the second limb portion 12B− of the second converter limb 12B switched out of circuit to continue to define a partially-conducting converter limb 12B.

During a sixth and final interval 34 ₆ the first controller 32 operates the primary switching element Sw₆ in the second limb portion 12B− of the second converter limb 12B to switch the second limb portion 12B− into circuit and thereby define, along with the already switched into circuit first limb portion 12B+, a fully-conducting converter limb 12B. At the same time the first controller 32 continues to leave the second limb portion 12A− of the first converter limb 12A switched into circuit and the first limb portion 12A+ switched out of circuit to continue to define a partially-conducting converter limb 12A. The first controller 32 also, at the same time, leaves the first limb portion 12C+ of the third converter limb 12C switched into circuit while operating the switching element Sw₂ of the second limb portion 12C− of the third limb portion 12C to switch the second limb portion 12C− out of circuit and thereby define a partially-conducting converter limb 12C.

It follows that the first controller 32 sequentially defines single, individual first, second, third, fourth, fifth and sixth fully-conducting converter limbs 12A, 12C, 12B, 12A, 12C, 12B during corresponding first, second, third, fourth, fifth and sixth intervals 34 ₁, 34 ₂, 34 ₃, 34 ₄, 34 ₅, 34 ₆ of a complete operating cycle 36 of the converter 10.

The converter 10 also includes a second controller 38 that is arranged in communication with the first controller 32 and each of the chain-link converters 24A+, 24A−, 24B+, 24B−, 24C+, 24C−. The second controller 38 is similarly a programmable device, such as a microcontroller. Although in the embodiment described, the first and second controllers 32, 38 are shown as separate items, they may in other embodiments of the invention form individual parts or a single part of a larger controller or controller arrangement.

Returning to the embodiment shown, the second controller 38 is programmed to:

-   -   (a) obtain a respective AC current demand phase waveform I_(A),         I_(B), I_(C) for each converter limb 12A, 12B, 12C which the         corresponding converter limb 12A, 12B, 12C is required to track,         and a DC current demand I_(DC) which each converter limb 12A,         12B, 12C is also required to track; and     -   (b) carry out mathematical optimization to determine an optimal         limb portion current I_(A+), I_(A−), I_(B+), I_(B−), I_(C+),         I_(C−) for each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−         that the limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− must         contribute to track the corresponding required AC current demand         phase waveform I_(A), I_(B), I_(C) and the required DC current         demand I_(DC).

The second controller 38 is also further programmed to (c) carry out mathematical optimization to provide optimal limb portion voltage sources V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−), with these principal steps (a), (b) and (c) being illustrated in a first flow diagram 40 shown in FIG. 4.

As set out above, the second controller 38 is programmed to first obtain a respective AC current demand phase waveform I_(A), I_(B), I_(C) for each converter limb 12A, 12B, 12C which each converter limb 12A, 12B, 12C is required to track, and then obtain a DC current demand I_(DC) which the converter limbs 12A, 12B, 12C are also required to track.

The various AC current demand phase waveforms I_(A), I_(B), I_(C) and the DC current demand I_(DC) may be obtained directly from a higher-level controller (not shown) within a converter or from some other external entity. Alternatively the converter 10 may obtain it directly by carrying out its own calculations.

The second controller 38 is also programmed to, as a second step (and as indicated by a first process box 42 in the first flow diagram 40), carry out mathematical optimization to determine an optimal limb portion current I_(A+), I_(A−), I_(B+), I_(B−), I_(C+), I_(C−) for each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− that the limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− must contribute to track the corresponding required AC current demand phase waveform I_(A), I_(B), I_(C) and the required DC current demand I_(DC).

The second controller 38 is programmed to carry out such mathematical optimization by creating an equivalent converter configuration 100, as shown in FIG. 5, which represents the flow of current through the corresponding converter 10 of the invention.

The equivalent converter configuration 100 includes similar features to the converter 10 of the invention and these like features share the same reference numerals. To that end the equivalent converter configuration 100 includes three converter limbs 12A, 12B, 12C, each of which corresponds to a respective phase A, B, C of the converter 10 of the invention.

In the equivalent converter configuration 100 each converter limb 12A, 12B, 12C similarly extends between first and second DC terminals 14, 16, and each converter limb 12A, 12B, 12C includes a first limb portion 12A+, 12B+, 12C+ and a second limb portion 12A−, 12B−, 12C−. Each pair of first and second limb portions 12A+, 12A−, 12B+, 12B−, 12C+, 12C− in each converter limb 12A, 12B, 12C is separated by a corresponding AC terminal 18A, 18B, 18C.

The equivalent converter configuration 100 also represents the respective AC current demand phase waveforms I_(A), I_(B), I_(C) that each converter limb 12A, 12B, 12C is required to track, e.g. match as closely as possible, and the DC current demand I_(DC) that the converter limbs 12A, 12B, 12C are also required to track.

In practice each converter limb 12A, 12B, 12C also operates within the constraints of the corresponding AC voltage phase waveforms V_(A), V_(B), V_(C) of the AC network 22, as well as a DC voltage V_(DC) of the DC electrical network 20, to which the converter 10 is, in use, connected, and so the equivalent converter configuration 100 may also represent these elements.

The second controller 38 is programmed to create an equivalent converter configuration 100 which represents the flow of current through the converter 10 by mapping possible current flow paths through the converter 10.

One way in which the possible current flow paths through the converter 10 may be mapped is by conducting a Kirchhoff analysis of the equivalent converter configuration 100 obtain the following equations:

I _(A)=α_(A) ⁺ I _(A+)−α_(A) ⁻ I _(A−)

I _(B)=α_(B) ⁺ I _(B+)−α_(B) ⁻ I _(B−)

I _(C)=α_(C) ⁺ I _(C+)−α_(C) ⁻ I _(C−)

I _(DC+)=α_(A) ⁺ I _(A+)+α_(B) ⁺ I _(B+)+α_(C) ⁺ I _(C+)

I _(DC−)=α_(A) ⁻ I _(A−)+α_(B) ⁻ I _(B−)+α_(C) ⁻ I _(C−)

where

-   -   the binary variables α_(k) ^(±) indicate whether a given limb         portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− is switched into         circuit (α_(k) ^(±)=1) or out of circuit (α_(k) ^(±)=0), i.e.         α_(A) ⁺, α_(A) ⁻, α_(B) ⁺, α_(B) ⁻, α_(C) ⁺, α_(C) ⁻ represent         the state of the corresponding primary switching element Sw₁,         Sw₂, Sw₃, Sw₄, Sw₅, Sw₆ in each limb portion 12A+, 12A−, 12B+,         12B−, 12C+, 12C− of the converter 10 (details of which are         provided to the second controller 38 by the first controller         32);     -   I_(DC+) is the sum of currents in the first limb portions 12A+,         12B+, 12C+, i.e. as shown in FIG. 3;     -   I_(DC−) is the sum of currents in the second limb portions 12A−,         12B−, 12C−, i.e. as also shown in FIG. 3; and

I _(DC+) =I _(DC−) =I _(DC)

The preceding equations are then combined and simplified into

I _(A)=α_(A) ⁺ I _(A+)−α_(A) ⁻ I _(A−)

I _(B)=α_(B) ⁺ I _(B+)−α_(B) ⁻ I _(B−)

I _(C)=α_(C) ⁺ I _(C+)−α_(C) ⁻ I _(C−)

I _(DC)=α_(A) ⁺ I _(A+)+α_(B) ⁺ I _(B+)+α_(C) ⁺ I _(C+)

The possible current flow paths through the converter 10 are then mapped by expressing the latter equations in a matrix form, i.e.:

${\overset{\overset{A}{}}{\begin{pmatrix} \alpha_{A}^{+} & {- \alpha_{A}^{-}} & 0 & 0 & 0 & 0 \\ 0 & 0 & \alpha_{B}^{+} & {- \alpha_{B}^{-}} & 0 & 0 \\ 0 & 0 & 0 & 0 & \alpha_{C}^{+} & {- \alpha_{C}^{-}} \\ \alpha_{A}^{+} & 0 & \alpha_{B}^{+} & 0 & \alpha_{C}^{+} & 0 \end{pmatrix}} \cdot \overset{\overset{x}{}}{\begin{pmatrix} I_{A +} \\ I_{A -} \\ I_{B +} \\ I_{B -} \\ I_{C +} \\ I_{C -} \end{pmatrix}}} = \overset{\overset{b}{}}{\begin{pmatrix} I_{A} \\ I_{B} \\ I_{C} \\ I_{DC} \end{pmatrix}}$

such that A is a matrix which maps the possible current flow paths provided by the limb portions 12A+, 12A−, 12B+, 12B−, 12C+, 12C−.

Other equivalent converter configurations and corresponding analysis techniques are, however, also possible.

The second controller 38 is also programmed to carry out mathematical optimization by applying a current weighting to the relative current contribution provided by each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−. The respective current weighting for each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− is determined according to measured operating parameters of the converter 10 during its operation. The various current weightings can be determined throughout operation of the said converter 10 so as to permit an updating of the current weightings, e.g. in response to changing environmental conditions. As a result the various current weightings can vary as the converter 10 operates.

During normal operation of the converter 10 an identical current weighting is applied to each limb portion current I_(A+), I_(A−), I_(B+), I_(B−), I_(C+), I_(C−).

However, when the converter 10 is operating under certain conditions, e.g. an abnormal operating condition, a different current weighting may be applied to the current contribution, i.e. the limb portion current I_(A+), I_(A−), I_(B+), I_(B−), I_(C+), I_(C−), provided by at least one limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−. For example, a larger current weighting may be applied to the optimal limb portion current I_(A+), I_(A−), I_(B+), I_(B−), I_(C+), I_(C−) that a particular limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C must contribute, so as to reduce an actual limb portion current that the said limb portion contributes relative to an actual current contribution of each of the other limb portions, which are otherwise all the same as one another.

In addition to the foregoing the second controller 38 is programmed to carry out mathematical optimization to determine a minimum individual limb portion current I_(A+), I_(A−), I_(B+), I_(B−), I_(C+), I_(C−) that each of the limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− must contribute so as to track the corresponding required AC current demand phase waveform I_(A), I_(B), I_(C) and the required DC current demand I_(DC)-One way in which minimum individual limb portion currents I_(A+), I_(A−), I_(B+), I_(B−), I_(C+), I_(C−), i.e. x in the A·x=b equation set out above, may be determined, and the aforementioned individual current weightings applied to the minimal individual limb portion currents I_(A+), I_(A−), I_(B+), I_(C+), I_(C−), is by solving a nonlinear optimization of the general form:

${\min\limits_{x}J_{Current}} = {{\Psi \left( {x\left( t_{1} \right)} \right)} + {\int_{t_{0}}^{t_{1}}{{f\left( {{x(t)},t} \right)}\ {t}}}}$

subject to the equality constrained equation of the form:

A·x=b

where

-   -   J_(Current) is the current objective function to be minimized;     -   Ψ is the current weighting at time t₁;     -   f is the current cost function which in the embodiment described         includes a current weighting matrix Q₁;     -   x is the transpose of [I_(A+), I_(A−), I_(B+), I_(B−), I_(C+),         I_(C−)], i.e. [I_(A+), I_(A−), I_(B+), I_(B−), I_(C−)] reflected         in a column vector;     -   t₀ is the time at which a particular period of control of the         converter 10 starts; and     -   t₁ is the time at which a particular period of control of the         converter 10 ends.

The current weighting matrix Q₁ is determined according to measured operating parameters of the converter 10, and may be so determined throughout the operation of the converter 10, such that it can vary as the said converter 10 is controlled in response to changes in the operation of the converter 10.

When subject only to an equality constrained equation, as mentioned above, the Lagrangian (or the method of Lagrange multipliers) is a technique for solving the above-identified nonlinear optimization in order to find local minima of the current objective function J_(Current). It may also be solved using other optimization algorithms, including iterative and programming algorithms.

As a general optimal control problem, the aforementioned nonlinear optimization could additionally include one or more inequality constraints in which case it could be solved by using the further method of Hamiltonian (Pontryagin's minimum principle).

One example of such an inequality constraint is:

${C\overset{\overset{x}{}}{\begin{pmatrix} I_{A +} \\ I_{A -} \\ I_{B +} \\ I_{B -} \\ I_{C +} \\ I_{C -} \end{pmatrix}}} \leq \overset{\overset{d}{}}{\begin{pmatrix} I_{A +}^{\max} \\ I_{A -}^{\max} \\ I_{B +}^{\max} \\ I_{B -}^{\max} \\ I_{C +}^{\max} \\ I_{C -}^{\max} \end{pmatrix}}$

where

-   -   C is a matrix which maps possible maximum current flow paths         provided by the limb portions 12A+, 12A−, 12B+, 12B−, 12C+,         12C−; and     -   d is a vector representing of the maximum desired current in         each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−.

In either case the minimum individual limb portion currents I_(A+), I_(A−), I_(B+), I_(B−), I_(C+), I_(C−) may also be determined by solving a nonlinear optimization of the form

$\max\limits_{x}{\left\{ {- J_{Current}} \right\}.}$

Meanwhile, as mentioned above, the second controller 38 is also programmed to carry out mathematical optimization to provide an optimal limb portion voltage source V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−) for each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− to achieve the corresponding mathematically optimized minimum limb portion current I_(A+), I_(A−), I_(B+), I_(B−), I_(C+), I_(C−). In other embodiments of the method of the invention, however, such mathematical optimization of the limb portion voltage sources need not take place.

The second controller 38 is programmed to carry out mathematical optimization to provide optimal limb portion voltage sources V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−) by creating an equivalent converter configuration 100 which represents voltage conditions in the converter 10.

Representing the voltage conditions in the converter 10 portrayed in the equivalent converter configuration 100 additionally includes mapping a limb portion voltage source V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−) and an inductive component for each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−.

In the embodiment described, each limb portion voltage source V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−) corresponds to a respective chain-link converter 24A+, 24A−, 24B+, 24B−, 24C+, 24C− which is switchable into and out of the corresponding limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− via operation of the corresponding primary switching element Sw₁, Sw₂, Sw₃, Sw₄, Sw₅, Sw₆. Each limb portion voltage source V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−) is therefore variable in magnitude between zero (i.e. equivalent to being switched out of the corresponding limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−) and an upper voltage limit.

Meanwhile an inductive component for each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− within the equivalent converter configuration 100 represents the inductance associated with the corresponding limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− of the actual converter 10. Such inductances do not include a passive limb inductor within each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− since they are no longer needed to control the level of circulating current between the converter limbs 12A, 12B, 12C. Instead, the respective inductances take the form of a phase inductance 44A, 44B, 44C and a DC line inductance 46 (each of which may be made up of a physical passive inductor component and any stray inductance within the associated electrical structure of the converter), and a very small remaining stray inductance within the corresponding limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−.

The aforementioned inductive component of each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− is represented in the equivalent converter configuration 100 as an inductive voltage portion U_(A+), U_(A−), U_(B+), U_(B−), U_(C+), U_(C−) that is made up of the voltage arising from the flow of current through the aforementioned inductance, i.e. phase inductance 44A, 44B, 44C and DC line inductance 46 only, associated with a corresponding limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−.

In other embodiments of the invention representing of the voltage conditions in the converter 10 may additionally include mapping a resistive component for each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−.

Such a resistive component represents the resistance associated with a given limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−, and similarly may take the form of a resistor within a given limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−, i.e. a limb portion resistance, or the form of a resistance electrically associated with a given limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−, e.g. a phase resistance and/or a DC line resistance.

Mapping the limb portion voltage sources V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−) and inductive voltage portions U_(A+), U_(A−), U_(B+), U_(B−), U_(C+), U_(C−) again similarly includes conducting a Kirchhoff analysis of the equivalent converter configuration 100, although other equivalent converter configurations and corresponding analysis techniques are also possible. In applying the Kirchhoff analysis the following equation, in matrix form, is obtained:

${{M_{V} \cdot \begin{pmatrix} V_{A +} \\ V_{A -} \\ V_{B +} \\ V_{B -} \\ V_{C +} \\ V_{C -} \end{pmatrix}} - {M_{U} \cdot \begin{pmatrix} U_{A +} \\ U_{A -} \\ U_{B +} \\ U_{B -} \\ U_{C +} \\ U_{C -} \\ V_{DC} \\ V_{AB} \\ V_{CB} \end{pmatrix}}} = \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix}$

where:

$M_{V} = \begin{pmatrix} 1 & 1 & {- 1} & {- 1} & 0 & 0 \\ 0 & 0 & 1 & 1 & {- 1} & {- 1} \\ 0 & 0 & 0 & 0 & 1 & 1 \\ 1 & 0 & {- 1} & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & {- 1} & 0 \end{pmatrix}$

i.e. M_(V) is a matrix which maps the position of the limb portion voltage sources V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−) within the particular converter structure;

$M_{U} = \begin{pmatrix} 1 & {- 1} & {- 1} & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & {- 1} & {- 1} & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & {- 1} & {- 1} & 0 & 0 \\ 1 & 0 & {- 1} & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & {- 1} & 0 & 0 & 0 & {- 1} \end{pmatrix}$

i.e. M_(u) is a matrix which maps the position of the inductive voltage portions U_(A+), U_(A−), U_(B+), U_(B−), U_(C+), U_(C−) within the particular converter structure;

-   -   V_(DC) is the DC voltage, i.e. the voltage difference between         the first and second DC terminals 14, 16;     -   V_(AB) is the voltage difference between the first and second         converter limbs 12A, 12B; and     -   V_(CB) is the voltage difference between the third and second         converter limbs 12C, 12B.

The second controller 38 is further programmed to carry out mathematical optimization to provide an optimal limb portion voltage source V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−) for each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− by reducing any deviation in an actual measured limb portion current I′_(A+), I′_(A−), I′_(B+), I′_(B−), I′_(C+), I′_(C−) of a given limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− from the corresponding determined optimal limb portion current I_(A+), I_(A−), I_(B+), I_(B−), I_(C+), I_(C−) for the said given limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−.

The second controller 38 is still further programmed to calculate the inductive voltage portion U_(A+), U_(A−), U_(B+), U_(B−), U_(C+), U_(C−) for each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−. This calculation is based on the corresponding determined optimal limb portion currents I_(A+), I_(A−), I_(B+), I_(B−), I_(C+), I_(C−), together with the inductance associated with the corresponding limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−.

Thereafter the calculated inductive voltage portion U_(A+), U_(A−), U_(B+), U_(B−), U_(C+), U_(C−) is modified to drive the actual measured limb portion current I′_(A+), I′_(A−), I′_(B+), I′_(B−), I′_(C+), I′_(C−) to follow the corresponding determined optimal limb portion current I_(A+), I_(A−), I_(B+), I_(B−), I_(C+), I_(C−).

Such measuring and modification takes the form of a feedback loop which provides closed-loop control, as illustrated schematically by a second process box 48 in the first flow diagram 40 shown in FIG. 4. The feedback loop may additionally include a feed-forward element which seeks to predict desirable future values for one or more of the inductive voltage portions U_(A+), U_(A−), U_(B+), U_(B−), U_(C+), U_(C−) in order to improve the performance of the closed-loop control.

The calculated inductive voltage portion U_(A+), U_(A−), U_(B+), U_(B−), U_(C+), U_(C−) of each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− is utilised, as indicated by a third process box 50 in the first flow diagram 40, when carrying out the aforementioned mathematical optimization to provide the optimal limb portion voltage sources V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−). Such mathematical optimization also includes applying a voltage weighting to the relative voltage contribution provided by each limb portion voltage source V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−). The voltage weightings are determined according to measured operating parameters of the converter 10, and may be so determined throughout operation of the said converter 10. Such potentially repeated determination of the voltage weightings permits the ongoing optimization of the converter operation during, e.g. changing environmental conditions.

For example, during normal operation of the said particular converter structure an identical voltage weighting is applied to the limb portion voltage source V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−) of each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−.

However during, e.g. abnormal operating conditions, a different voltage weighting can be applied to the limb portion voltage source V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−) of one or more limb portions 12A+, 12A−, 12B+, 12B−, 12C+, 12C− to further alleviate the impact of, e.g. the abnormal operating conditions.

More particularly, the second controller 38 is programmed to carry out mathematical optimization to provide an optimal limb portion voltage source V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−) for each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− by determining a minimum individual limb portion voltage source V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−) for each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− that is required to achieve the corresponding minimum limb portion current I_(A+), I_(A−), I_(B+), I_(B−), I_(C+), I_(C−) previously determined.

One way in which minimum individual limb portion voltage sources V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−) (i.e. the minimum level of voltage a variable voltage source within a given limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− must provide) may be determined, and the aforementioned individual voltage weightings applied thereto, is by solving for x (where x is the transpose of [V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−)]) a nonlinear optimization of the general form:

${\min\limits_{x}J_{Voltage}} = {{\Psi \left( {x\left( t_{1} \right)} \right)} + {\int_{t_{0}}^{t_{1}}{{f\left( {{x(t)},t} \right)}\ {t}}}}$

subject to an equality constrained equation M_(V)·x=b, where b is known, of the form:

${M_{V} \cdot \overset{\overset{x}{}}{\begin{pmatrix} V_{A +} \\ V_{A -} \\ V_{B +} \\ V_{B -} \\ V_{C +} \\ V_{C -} \end{pmatrix}}} = \overset{\overset{b}{}}{M_{U} \cdot \begin{pmatrix} U_{A +} \\ U_{A -} \\ U_{B +} \\ U_{B -} \\ U_{C +} \\ U_{C -} \\ V_{DC} \\ V_{AB} \\ V_{CB} \end{pmatrix}}$

and where

-   -   J_(Voltage) is the voltage objective function to be minimized;     -   Ψ is the voltage weighting at time t₁     -   f is the voltage cost function which in the embodiment described         includes a voltage weighting matrix Q_(V);     -   t₀ is the time at which a particular period of control of the         converter 10 starts; and     -   t₁ is the time at which a particular period of control of the         converter 10 ends.

The voltage weighting matrix Q_(V) is similarly determined according to measured operating parameters of the converter 10, and may be so determined throughout the operation of the converter 10. As such it too can vary as the said converter 10 is controlled.

Solving the nonlinear optimization mentioned above may also be made subject to an inequality equation of the form:

C·x≦d

where

-   -   C is a matrix which maps the position of possible maximum limb         portion voltage sources in the limb portions 12A+, 12A−, 12B+,         12B−, 12C+, 12C−; and     -   d is a vector representing of the maximum desired voltage in         each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−.

An alternative second controller (not shown), which may instead be included in the converter 10, is similarly programmed to:

-   -   (a) obtain a respective AC current demand phase waveform I_(A),         I_(B), I_(C) for each converter limb 12A, 12B, 12C which the         corresponding converter limb 12A, 12B, 12C is required to track,         and a DC current demand I_(DC) which each converter limb 12A,         12B, 12C is also required to track; and     -   (b) carry out mathematical optimization to determine an optimal         limb portion current I_(A+), I_(A−), I_(B+), I_(B−), I_(C+),         I_(C−) for each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−         that the limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− must         contribute to track the corresponding required AC current demand         phase waveform I_(A), I_(B), I_(C) and the required DC current         demand I_(DC).

The aforementioned steps are again, similarly indicated by a first process box 42 in a second flow diagram 60 shown in FIG. 6(a).

Thereafter, however, the alternative second controller is programmed to apply a control algorithm to directly establish optimal limb portion voltage sources V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−) from each of the corresponding determined minimum limb portion current I_(A+), I_(A−), I_(B+), I_(B−), I_(C+), I_(C−), i.e. as shown by a single fourth process box 62 in the second flow diagram 60.

Applying such a control algorithm includes reducing any deviation in the actual measured limb portion current I′_(A+), I′_(A−), I′_(B+), I′_(B−), I′_(C+), I′_(C−) of a given limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− from the corresponding determined minimum limb portion current I_(A+), I_(A−), I_(B+), I_(B−), I_(C+), I_(C−) for the said given limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C−.

One way in which the deviation in the actual measured limb portion current I′_(A+), I′_(A−), I′_(B+), I′_(B−), I′_(C+), I′_(C−) of a given limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− from the corresponding determined minimum limb portion current I_(A+), I_(A−), I_(B+), I_(B−), I_(C+), I_(C−) may be reduced, and preferably eliminated, is by establishing a feedback loop 70 as shown schematically in FIG. 6(b).

In the embodiment shown the feedback loop 70 compares a respective actual measured limb portion current I′_(A+), I′_(A−), I′_(B+), I′_(B−), I′_(C+), I′_(C−) with the corresponding determined minimum limb portion current I_(A+), I_(A−), I_(B+), I_(B−), I_(C+), I_(C−) and calculates a corresponding limb portion error e_(A+), e_(A−), e_(B+), e_(B−), e_(C+), e_(C−). The feedback loop 70 then applies a correction factor K to each limb portion error e_(A+), e_(A−), e_(B+), e_(B−), e_(C+), e_(C−) to thereby establish directly the corresponding limb portion voltage source V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−) which is required to drive the error e_(A+), e_(A−), e_(B+), e_(B−), e_(C+), e_(C−) towards zero.

The correction factor K may take the form of a control system matrix, such as a gain matrix (not shown), which sets out individual correction factors that each limb portion error e_(A+), e_(A−), e_(B+), e_(B−), e_(C+), e_(C−) is, e.g. multiplied by in the case of a gain matrix, to establish the corresponding limb portion voltage source V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−).

One way in which such individual correction factors may be established is by creating an equivalent converter configuration that represents the voltage conditions in the particular three-phase converter structure under control and thereafter considering the dynamics of such an equivalent converter configuration.

More particularly, in relation to the embodiment described hereinabove, the foregoing steps may be achieved by creating the equivalent converter configuration 100 shown in FIG. 5 and mapping a limb portion voltage source V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−) and an inductive component for each limb portion 12A+, 12A−, 12B+, 12B−, 12C+, 12C− in the equivalent converter configuration 100.

Thereafter such mapping may include conducting a Kirchhoff analysis of the equivalent converter configuration 100 (although other equivalent converter configurations and corresponding analysis techniques are also possible) that applies Kirchhoff's current and voltage laws to describe the dynamics of the equivalent converter configuration 100 as:

$v = {{M\frac{I}{t}} + {N\; \xi}}$

where:

-   -   v is the transpose of [V_(A+), V_(A−), V_(B+), V_(B−), V_(C+),         V_(C−)],     -   M is a coupled-inductance matrix which maps the inductive         component of each limb portion, and more particularly maps each         of the phase and DC line inductances associated with each limb         portion; e.g.

${M = {10^{- 3}\begin{pmatrix} 3 & {- 2} & 1 & 0 & 1 \\ {- 1} & 2 & 1 & 0 & 1 \\ 1 & 0 & 3 & {- 2} & 1 \\ 1 & 0 & {- 1} & 2 & 1 \\ {- 1} & 2 & {- 1} & 2 & 1 \\ 3 & {- 2} & 3 & {- 2} & 1 \end{pmatrix}}};$

-   -   I is the transpose of [I′_(A+), I′_(A−), I′_(B+), I′_(B−),         I′_(C+), I′_(C−) ], i.e. the transpose of a currents vector         representing the actual measured limb portion currents I′_(A+),         I′_(A−), I′_(B+), I′_(B−), I′_(C+), I′_(C−);     -   N is an input voltage matrix which maps the position of various         input voltages within the particular converter structure, e.g.

${N = {\frac{1}{6}\begin{bmatrix} 3 & {- 4} & 2 \\ 3 & 4 & {- 2} \\ 3 & 2 & 2 \\ 3 & {- 2} & {- 2} \\ 3 & 2 & {- 4} \\ 3 & {- 2} & 4 \end{bmatrix}}};$

and

-   -   ξ is an input voltages vector representing external         disturbances, e.g.

$\xi = \begin{bmatrix} V_{DC} \\ V_{AB} \\ V_{CB} \end{bmatrix}$

where

-   -   V_(DC) is the DC voltage, i.e. the voltage difference between         the first and second DC terminals 14, 16;     -   V_(AB) is the voltage difference between the first and second         converter limbs 12A, 12B; and     -   V_(CB) is the voltage difference between the third and second         converter limbs 12C, 12B.

In this way, conducting the aforesaid Kirchhoff analysis makes it possible to take into account all of the factors mentioned above relating to the converter 10, i.e. M, I, N, ξ, when considering what impact a change in one or more individual limb portion voltage sources V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−) will have, e.g. on the actual measured limb portion current I′_(A+), I′_(A−), I′_(B+), I′_(B−), I′_(C+), I′_(C−). This ability renders the alternative second controller robust against controller uncertainties and modelling errors.

Moreover, as a result it is possible thereafter to establish each of the individual correction factors by considering what change needs to be made to a given individual limb portion voltage source V_(A+), V_(A−), V_(B+), V_(B−), V_(C+), V_(C−) to desirably alter the corresponding limb portion current provided by the converter 10 under control, i.e. the corresponding actual measured limb portion current I′_(A+), I′_(A−), I′_(B+), I′_(B−), I′_(C+), I′_(C−), in order to drive the actual measured limb portion current I′_(A+), I′_(A−), I′_(B+), I′_(B−), I′_(C+), I′_(C−) towards the determined minimum limb portion current I_(A+), I_(A−), I_(B+), I_(B−), I_(C+), I_(C−), i.e. in order to reduce the corresponding limb portion error e_(A+), e_(A−), e_(B+), e_(B−), e_(C+), e_(C−) towards zero.

Once such individual correction factors have been established for the converter 10, e.g. at initial design and commissioning stages, there is not normally a need to determine them again. As a result the feedback loop 70 involves minimal computational effort since in each cycle it is simply required to multiply a given limb portion error e_(A+), e_(A−), e_(B+), e_(B−), e_(C+), e_(C−) by the corresponding individual correction factor which has already been determined. 

1. A converter, for use in high voltage direct current power transmission, comprising: three converter limbs, each corresponding to a respective phase of the converter, each extending between first and second DC terminals and each including first and second limb portions separated by an AC terminal, each limb portion including a chain-link converter operable to provide a stepped variable voltage source and a primary switching element to selectively switch the respective limb portion into and out of circuit; and a first controller programmed to selectively operate for one converter limb at a time the primary switching element in each limb portion thereof to simultaneously switch both the first and second limb portions into circuit and thereby define a fully-conducting converter limb to sequentially route via each said fully-conducting converter limb a DC current demand between the first and second DC terminals.
 2. A converter according to claim 1 wherein the first controller is programmed to sequentially define fully-conducting converter limbs at regular intervals of around 60 electrical degrees.
 3. A converter according to claim 1 wherein the first controller is additionally programmed, while selectively operating for a given converter limb the primary switching element in each limb portion thereof to simultaneously switch both the first and second limb portions into circuit and thereby define a fully-conducting converter limb, to concurrently operate for each other converter limb the primary switching element in one or both limb portions thereof to switch a single limb portion into circuit and thereby define a partially-conducting converter limb to direct respective AC current demand phase waveforms towards a given AC terminal whereby the respective AC current demand phase waveforms sum to zero.
 4. A converter according to claim 1 further including a second controller programmed to: (a) obtain a respective AC current demand phase waveform for each converter limb which the corresponding converter limb is required to track, and a DC current demand which each converter limb is also required to track; and (b) carry out mathematical optimization to determine an optimal limb portion current for each limb portion that the limb portion must contribute to track the corresponding required AC current demand phase waveform and the required DC current demand.
 5. A converter according to claim 4 wherein the second controller is programmed to carry out mathematical optimization by creating an equivalent converter configuration which represents the flow of current through the converter.
 6. A converter according to claim 5 wherein the second controller is programmed to create an equivalent converter configuration which represents the flow of current through the converter by mapping possible current flow paths through the converter.
 7. A converter according to claim 1 wherein the second controller is programmed to carry out mathematical optimization by applying a current weighting to the relative current contribution provided by a plurality of limb portions.
 8. A converter according to claim 7 wherein the second controller is programmed to determine the or each weighting according to measured operating parameters of the converter.
 9. A converter according to claim 7 wherein when controlling the converter under a particular operating condition the second controller is programmed to apply a weighting by applying a different weighting to at least one limb portion such that the or each said limb portion provides a different contribution to the other limb portions.
 10. A converter according to claim 4 wherein the second controller is programmed to carry out mathematical optimization to determine one or more minimum individual limb portion currents that the corresponding limb portion must contribute to track the corresponding required AC current demand phase waveform and the required DC current demand.
 11. A converter according to claim 4 wherein the second controller is further programmed to carry out mathematical optimization to provide optimal limb portion voltage sources. 